It has been nearly 30 years since the last major retrospective of Manet's work, so a new blockbuster in Paris this spring must be an important event. As indeed it is. Forget Monet, recently on show at the Grand Palais, when it comes to the really greats of art history, Edouard Manet is up amongst the best. You can never see enough of him.

The problem for the curators is how to say something new, especially after the comprehensiveness of the 1983 show. But then why the need to say anything novel at all? After a generation-and-a-half, there will be plenty who didn't see the last effort, and some who did, who are more than happy to just stand and gaze at the deep blacks, brilliant whites and those frank faces. However you cut him, Manet has the extraordinary quality of relating to the viewer with the warmth of his vision, as well as its artifice, and wherever you place him, he is great above all because of the radicalism of his technique and the individuality of his view.

That is not how the modern curator sees it, of course. And so at the Musée d'Orsay we are treated to a studiedly different approach to the traditional retrospective. Manet is no longer seen simply as the great "precursor" of the modern in his brushwork, his composition and his colouring. Far from it. Here he is viewed as a man of his age, who owed much to his early training under Thomas Couture, who bridged consciously the Romantic tradition with the modern, who kept showing at the Salons to the disgust of his impressionist contemporaries, and who fully engaged politically and culturally with the social and industrial revolutions of his time.

It's a perfectly valid approach. Thirty years ago, art critics were obsessed with the new and judged artists, from Renaissance to modernism, as to how far they were pioneers of painting progress. But Manet, while setting out to reinvent the art of his training, didn't see himself as a modernist in this sense and neither perhaps should we.

The exhibition starts with Fantin Latour's Homage to Delacroix, completed a year after the Romantic painter's death. It is the work which gave the curators the idea for the show. Here stands Manet together with Whistler and Baudelaire as preservers and modernisers of the great tradition, not its destroyer.

In the room that follows, Couture is given fair wind as Manet's teacher and influence, while, less successfully, the curators try to tie him in with Baudelaire's sustained espousal of a new painting of modern urban life to replace the history and moral painting of his time. Manet, as his impressionist colleagues were later to find, just wouldn't fit into the roles imposed by contemporaries. He was a painter who knew his worth, and like Turner before him and Picasso after, set himself to challenge the masters, not with a different vision but a new style. The brushwork to him was all and he used it to renew the art of his time, not to challenge the viewer but to make them see afresh.

You can witness it right at the beginning, in the first room, when two portraits by Couture and his young pupil are set side by side, the older man's Portrait d'Amédée Berger from 1852 and Manet's Portrait of a Man from three years later. Couture's work is forceful and proper, Manet's portrait is already loose in brushwork, the thin moustache delicately suggested, the eyes betraying the emotional life behind.

No artist has ever imbued his sitters with such a sense of hinterland. It's the way Manet does eyes. But it's a mystery as to how he achieves it. His men and women don't betray a particular emotion so much as a past. A wall of portraits of his fellow artist and later sister-in-law, Berthe Morisot (who has a wonderful portrait work of her own to show just how good an artist she was in the Manet manner, but with her own sensibility), leaves you stunned. It doesn't matter whether it is courtesans (a category the exhibition makes far too much of in an effort to make Manet a commentator of contemporary life) or women of fashion or men of letters, we are looking at an individual who has a real life behind them. It makes Manet, like Rembrandt, a supreme communicator of what makes us human.

Despite the scale of many of his pictures, Manet was too interested in the individual to monumentalise. It's what prevented him achieving success as a religious painter. The exhibition devotes a room to his Christian art. The ambition is there. The technique is fresh, but the pictures of Christ Insulted by the Soldiers and The Dead Christ with Angels remain an embarrassment. The Orsay puts this down to changing modern sensibilities but it's not really that. Manet doesn't feel the eternal or transcendental. To him it's more of a technical experiment, a reach to apply new ways with colour to an old tradition.

A fascinating section is devoted to his decision, having failed to impress the Salon with bigger compositions, to cut out bits from the canvases to intensify the viewer's gaze and produce more dramatic effects. Dead Matador – a work of fiercesome force – comes from a larger picture of the bull ring; a peasant drinking water has been cut from a bigger group, Les Gitanos.

Manet learnt from the Spanish art he so admired what depth a brilliant detail – a vase of flowers, a lemon or a plate of fish – could give to a picture. Conscious perhaps of the popularity of these Still Lifes, the curators here rather dismiss the works, although they formed a sizable proportion of his total output, as something he did to please the market. Not so; they were integral to his vision.

The attempt to define Manet in terms of themes this way palls after a bit, serving to confine the artist rather than to open him up, which is the one thing you shouldn't do with an artist as humane and as endlessly experimental as Manet. Take the explanations too seriously and you come out feeling dragooned into an academic view.

The answer is: don't. Ignore the section introductions. Just meander through the sections to be faced, slap on, by Olympia in all her nakedness, feeling the humour in her black servant, even more in the infamous Le Déjeuner sur l'Herbe, as the nude girl looks at you in amused tolerance as her male companions gas on beside her.

If the exhibition does not have the Mannheim The Execution of Maximilien it does have the sketchier and even more affecting version from Boston. If it lacks A Bar at the Folies Bergère and The Lunch on the Grass, shown together with such effect recently at the Courtauld, it does show a delightful oil sketch for the Folies Bergère from London.

One could have done with some of his great crowd scenes, but the portraits are here in number and, with so many of his finest works now resident in US museums, the Orsay has gathered a full bowl of plums to add to its own extensive holdings. Wonders indeed to behold. And if you desire the intellectualising, buy the catalogue with its essays and summaries of recent research (only in hardback unfortunately, priced €42).